The input variable of engineering structure inevitable has certain uncertainty. How to quantify the influence of those uncertainties on the uncertainty of structural response is an important issue in structural design. Non-probabilistic reliability importance analysis is one of the methods to quantify this influence when variable data information is insufficient. Although the method has great advantages for variables with insufficient data information, there is no efficient calculation method at present, and the excessive computational cost seriously hinders its application in actual engineering structures. In this paper, the multiplicative dimensional reduction method, Taylor series expansion and unary quadratic function are combined to put forward an efficient algorithm to estimate two non-probabilistic reliability importance indices. With the proposed method, all the calculation processes used to solve the extreme value of function are replaced by an approximate analytical solution. Since the proposed method is an approximate analytical solution, the calculation efficiency is extremely high. Three examples are investigated to verify the accuracy and efficiency of the proposed method.
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